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How to pick 'em (Posted on 2007-05-25) Difficulty: 2 of 5
I picked four integer numbers, none negative.

If I had told you their product, you would have known what the numbers were.

If I had told you instead the sum of their squares, you would also have known what the numbers were.

But if I had told you instead the sum of the numbers, you wouldn't have been able to tell what the numbers were.

Which were the numbers?

See The Solution Submitted by Federico Kereki    
Rating: 4.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: If duplicates are not allowed | Comment 6 of 8 |
(In reply to If duplicates are not allowed by Charlie)

If duplicates are not allowed

Any 4tuple 1,p1,p2,p3 has an  unique product if p1...,p3 are primes

To qualify as puzzle's solution we need to check  the  SUM of squares

e.g. 1 2  5 7    SofSQ= 1+4+25+49=79  ===

  Now check all possible 4tuples of distinct primes not over 7:

1 2 3 5  ==not 79
1 2 3 7   ==not 79
1 2 5 7  79
1 3 5 7 ==not 79
2 3 5 7  ==  not 79

so
1 2 5 7      is a valid solution of  the  puzzle
  

 

 


  Posted by Ady TZIDON on 2007-05-25 16:45:45
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